I'm pretty sure there were already in the 19th century people, like Helmholtz, Riemann etc. who saw themselves as Kantians, but nevertheless developed many of the techniques that later made GR possible (while acknowledging that they challenge Kant's own views) while preserving the core of Kant's theory. See my response above.
I'm pretty sure you don't find any passage in Kant where he says anything remotely like "Gallilean/neo-Newtonian space-time is absolutely true and forever true" (these words or the term "Euclidean geometry" didn't, I'm pretty sure, even exist back then). What is usually meant by ascribing him these views, I assume, is that he proceeds as if this were the case, i.e. he doesn't specify any empirical method for determining what is the proper geometry of space-time. These were developed in the nineteenth century. But even remarkably smart people, like Poincare, had troubles with figuring out how empirical evidence can help determine us the physically valid geometry of space-time (he thought it was necessarily conventional - a view falsified by general relativity), so I don't think this in any way makes Kant's enterprise as such questionable.
I find it interesting that you say: "although he might say we nevertheless have to experience time as constant and space in three dimensions". The physicist/philosopher/physiologist/mathematician Hermann von Helmholtz (who was, I think, very much inspired by Kant) wanted to prove that, given some basic measurement axioms (demanding constant curvature etc.), Euclidean geometry is necessarily the geometry of our internal perceptual manifolds (Kant's view is, I believe, essentially that these internal manifolds must have the same geometry as physical space-time). But it turned out that pseudo-spherical geometry also satisfies these axioms. So, although there is something, as far as your general description goes, to your 'defence' of Kant, and I think Helmholtz himself would've said that he's working within Kant's framework, it is still insufficient to vindicate everything that Kant said. I believe Helmholtz agreed, however, that our spatial imagination is three dimensional.
What I mean by "Kant's framework" is basically these three theses:
1. There are internal perceptual manifolds, distinct from mind-independent space-time.
2. Space adn time are preconditions of experience as such, i.e. we cannot ever get rid of them in our description of the world. They're not reducible to causal relations between events.
3. This doesn't require assuming Newtonian absolute space (relativism).
And Kant furthermore asserts that:
4. In addition to (1), there is no mind-independent space-time, space and time as such are mind-dependent. This means that our descriptions of the world are necessarily, e.g. Euclidean.
I don't think (1), (2), (3) are at all controversial, although only (2) and its consequences are a contribution of Kant himself, but (4) is, I'm pretty sure, quite universally rejected nowadays.
